Question

How do you find the fraction between $\dfrac{1}{3}$ and $\dfrac{1}{4}$.

Answer 1

Hint: We will take the L.C.M of denominator of both the fractions and thus we will convert the given two fraction into like fraction, therefore we can insert fraction or fractions between any two or more fractions.
Apply this concept to determine the solution of the question.

Complete step-by-step solution:
We are given as per question,
 we have to find the fraction between $\dfrac{1}{3}$ and $\dfrac{1}{4}$
So, for that taking the L.C.M. of denominator of both the fraction,
As L.C.M. of $\left( 3,4 \right)$ will be $12.$
So,
Multiply first fraction by $4$ in both numerator and denominator, and multiply numerator and denominator both of second fraction by $3.$
Hence,
$\dfrac{1}{3}=\dfrac{1\times 4}{4\times 3}=\dfrac{4}{12}$
And,
$\dfrac{1}{4}=\dfrac{1\times 3}{4\times 3}=\dfrac{3}{12}$
Hence,
We have to fractions,
As, $\dfrac{4}{12}$ and $\dfrac{3}{12}$
We can again rewrite the fractions as,
$\dfrac{4}{12}=\dfrac{8}{24}$
They are an equivalent fraction.
$\dfrac{3}{12}=\dfrac{6}{24}$
So,
Clearly in between $\dfrac{6}{24}$ and $\dfrac{8}{24}$ fraction $\dfrac{7}{24}$ can be written

Fraction $\dfrac{7}{24}$ will be in between $\dfrac{1}{4}$ and $\dfrac{1}{3}$

Note: We can also solve the above question by converting the given fraction into decimals.
Like
$\dfrac{1}{4}=0.25$
And $\dfrac{1}{3}=0.33$
So, we can say that,
In between $0.25$ and $0.33,0.26,0.27,0.28,0.29$ and $0.30$ can come,
We can also rewrite,
$0.26=\dfrac{26}{100}=\dfrac{13}{50}$
$0.27=\dfrac{27}{100}$
$\dfrac{0.28}{100}=\dfrac{28}{100}=\dfrac{7}{25}$
Thus, in such way we can also determine the fractions between $\dfrac{1}{3}$ and $\dfrac{1}{4}$